A corollary to the Evans-Griffith Syzygy theorem
A new algebraic criterion for shellability.
An improved Briancon-Skoda theorem with applications to the Cohen-Macaulayness of Rees algebras.
Arithmetically Cohen-Macaulay curves in P4 of degree 4 and genus 0.
Artin-Nagata properties and Cohen-Macaulay associated graded rings
Bifurcations in symplectic space
In this paper we take new steps in the theory of symplectic and isotropic bifurcations, by solving the classification problem under a natural equivalence in several typical cases. Moreover we define the notion of coisotropic varieties and formulate also the coisotropic bifurcation problem. We consider several symplectic invariants of isotropic and coisotropic varieties, providing illustrative examples in the simplest non-trivial cases.
Characterization of the Hilbert-Samuel polynomials of curve singularities
Cohen-Macaulay and Gorenstein property of rees algebras of non-singular equimultiple prime ideals.
Cohen-Macaulay Rees algebras and degrees of polynomial relations.
Cohen-Macaulayness of multiplication rings and modules
Let R be a commutative multiplication ring and let N be a non-zero finitely generated multiplication R-module. We characterize certain prime submodules of N. Also, we show that N is Cohen-Macaulay whenever R is Noetherian.
Cohen-Macauly Graphs.
Criteria for shellable multicomplexes.
Deformations of maximal Cohen-Macaulay modules.
Deforming syzygies of liftable modules and generalised Knörrer functors
Maps between deformation functors of modules are given which generalise the maps induced by the Knörrer functors. These maps become isomorphisms after introducing certain equations in the target functor restricting the Zariski tangent space. Explicit examples are given on how the isomorphisms extend results about deformation theory and classification of MCM modules to higher dimensions.
Divisorial cohomology vanishing on toric varieties.
(Generalized) filter properties of the amalgamated algebra
Let and be commutative rings with unity, a ring homomorphism and an ideal of . Then the subring and of is called the amalgamation of with along with respect to . In this paper, we determine when is a (generalized) filter ring.
Gluing Cohen-Macaulay modules with applications to quasihomogeneous complete intersections with isolated singularities.
Gorenstein property and symmetry for one dimensional local Cohen-Macaulay rings.
Hilbert functions, Castelnuovo-Mumford regularity and uniform Artin-Rees numbers.
Indecomposable Cohen-Macaulay modules and irreducible maps